I assume you will be taking I-90 when you get past Chicago. That will take you right passed the
Spam Museum in Austin, MN, and the
Corn Palace in Mitchell, SD.
And when you are in the Custer area, also check out
Jewel Cave National Monument. The
South Dakota Air and Space Museum is located at Ellsworth Air Force Base. I can't remember the name of the place, but we also did a tour of a gold mine there, and then "pan for gold" (a pan with the rock and sand already in it, along with a couple specks of gold). There's also a lot there at Custer to do and see. Our kids were just fascinated by a prairie dog village in the park, and we ended up staying there for a couple hours. There's bison and
wild ass at the park also to go see.
It has been a long time since I've been out that way, but we spent a week there, and could have stayed another week, and still not see everything. It got to the point that our last full day there, we decided to split up, because my brother and his family wanted to go out to Deadwood, and we wanted to go explores the caves. But there's so much to do out there that you probably won't get to see everything.
As for overnights on the way there and back, We just made reservations for the trip there and the trip home. We're in the Twin Cities area, so it was just one overnight on the way and back (could have pushed through, but with 4 kids not yet in school - 2 mine and 2 my brothers felt it better to stop for the night). We stopped at a campground in Mitchell, SD on the way there, and then in Chamberlain. SD on the way back.